SATHEE: Rotation 4 Question 4

Rotation 4 Question 4

5. A thin ring of mass $2 k g$ and radius $0.5 m$ is rolling without slipping on a horizontal plane with velocity $1 m / s$ . A small ball of mass $0.1 k g$ , moving with velocity $20 m / s$ in the opposite direction, hits the ring at a height of $0.75 m$ and goes vertically up with velocity $10 m / s$ . Immediately after the collision,

(2011)

(a) the ring has pure rotation about its stationary $C M$

(b) the ring comes to a complete stop

(d) there is no friction between the ring and the ground

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Answer:

Correct Answer: 5. $(a, c)$

Solution:

The data is incomplete. Let us assume that friction from ground on ring is not impulsive during impact.

From linear momentum conservation in horizontal direction, we have

$\begin{aligned} (- 2 \times 1) + & (0.1 \times 20) & - v e \\ = (0.1 \times 0) + (2 \times v) & + v e \end{aligned}$

Here, $v$ is the velocity of $C M$ of ring after impact. Solving the above equation, we have $v = 0$

Thus, CM becomes stationary.

$∴$ Correct option is (a).

Linear impulse during impact

(i) In horizontal direction

$J_{1} = Δ p = 0.1 \times 20 = 2 N - s$

(ii) In vertical direction $J_{2} = Δ p = 0.1 \times 10 = 1 N$ -s Writing the equation (about $C M$ )

Angular impulse $=$ Change in angular momentum

We have,

$1 \times \frac{\sqrt{3}}{2} \times \frac{1}{2} - 2 \times 0.5 \times \frac{1}{2} = 2 \times (0.5)^{2} ω - \frac{1}{0.5}$

Solving this equation $ω$ comes out to be positive or $ω$ anti-clockwise. So just after collision rightwards slipping is taking place.

Hence, friction is leftwards.

Therefore, option (c) is also correct.

पिछला

अगला

Rotation 4 Question 4

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

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अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Rotation 4 Question 4

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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